||Electric field dependence of magnetic, electronic, and structural properties in a Pd bilayer film on MgO (001) is investigated by using the first-principles electronic structure calculations within density functional theory. We find that, due to the lattice mismatch of 6.7 %, a ferromagnetic ground state is stabilized at zero electric field on an otherwise paramagnetic Pd with the spin magnetic moments of m = 0.31 and 0.34 mu(B) in surface and interface Pd, respectively. The application of an external electric field, E, causes the Pd magnetic moments to be modulated in a site- and electric field-dependent manner. As the external electric field pointing inward to the Pd surface is increased up to the critical value of 1.3 V/angstrom, the surface Pd moment is barely changed while the interfacial Pd moment increases linearly with E. Above this critical electric field, the moments of both the interfacial and surface Pd atoms exhibit nonlinear increase with E and reach up to 0.34 (surface) and 0.41 (interface) mu(B) at E = 2.5 V/angstrom. When the electric field direction is inverted, a similar dependence on E is obtained for both Pd atoms at the critical electric field value of -0.5 V/angstrom. The peculiar behavior of the induced magnetic moments is explained by combining the linearized Stoner and itinerant conduction models. We reveal that this prominent magnetoelectric effect is due to the modulated charge occupancy of Pd 4d-states in the minority spin channel in which the d(z2) and d(x2 y2) orbitals play crucial roles.